It's possible. If there are some unspent outputs on old keys included n that backup.
To be 100% sure the old backup cannot be used to steal some (or all) of your money, just create the new one and send all the coins to it. But keep the old one in case someone send you bitcoins to one of the old addresses.
There is no need to save the the old wallet or address.
Just dump the private key on old wallet and import to the new one.